# COMEDK Sample Paper for Maths 2013

The COMEDK UGET 2013 sample paper contain 3 papers:

- Physics
- Chemistry
- Mathematics

Each section have 60 questions and for each correct answer there is one mark.This question paper have the solved answers which will help the students to get ideas about the paper pattern, question distribution and the marks allocated for each section.

The students can download COMEDK UGET 2013 sample papers to refer to the previous year questions, practice them and get better scores in order to get admission in their favourite engineering institute.

**COMEDK Sample Paper for Maths 2013**

*MATHEMATICS*

1. The equation 2×2 + 3x + 1 = 0 has

A. rational root

B. irrational root

C. equal root

D. none of the above

2. A bag contains 6 red, 5 green, and 7 white balls. The probability of choosing a red or a

white ball is

A. 1/3

B. 11/13

C. 13/18

D. 3/8

3. ∫ (x + 2)/(x + 4) dx is equal to

A. 1/2[tan -1(x – 2/x)] +c

B. tan -1x + c

C. 1/2[tan -1(2/x)] + c

D. none of the above

4. The length intercepted on the line 3x + 4y + 1 = 0 by the circle (x – 1)2 + (y – 4)2 = 25 is

A. 3

B. 4

C. 5

D. 6

5. The period of the function cos [(3/5)α] – sin [(2/7)α] is

A. 7π

B. 10π

C. 70π

D. 3π

6. The minimum value of xx is attained when x is equal to

A. – e

B. + e

C. e ^2

D. 1/e

7. If a, b, c and u, v, w are complex numbers representing the vertices of two triangles such that

c = (1 – r)a + rb and w = (1 – r)u + rv, where r is a complex number, then the two triangles are

A. similar

B. congruent

C. equal in area

D. equal bases

8. In a triangle ABC, if r and R are the in-radius and circum-radius respectively, then

(a cos A+ b cos B + c cos C)/(a + b + c) is

A. r/R

B. R/r

C. R2/r

D. r2/R

9. ∫ [(x + sinx)/(1 + cosx)] dx is equal to

A. x tan(x/2)

B. x tan(x/2) + c

C. log (1 + cosx) + c

D. x log (cos x) + c

10. The differential coefficient of f [log(x)] when f(x) log x is

A. x log x

B. x/(log x)

C. 1/(x log x)

D. (log x)/x

11. If x = 9 sin 2θ (1 + cos 2θ) and y = b cos 2θ (1 – cos 2θ), then the value of dy/dx is

A. (b tan θ)/a

B. a/(b tan θ)

C. (a tan θ)/b

D. ab tan θ

12. The number of solution of the equation (tan x + sec x = 2 cos x) lying in the interval (0, 2π)is

A. 0

B. 1

C. 2

D. 3

13. If θ and φ are angles in the first quadrant such that tan θ = 1/7 and sin φ = 1/√10, then

A. θ + 2φ = 90o

B. θ + 2φ = 60o

C. θ + 2φ = 30o

D. θ + 2φ = 45o

14. If a cos 2θ + b sin 2θ = c has a and b as its solution, then the value of tan α + tan β is

A. (c + a)/2b

B. 2b/(c + a)

C. (c – a)/2b

D. b/(c + a)

15. The perimeter of a certain sector of a circle is equal to the length of the arc of a semi-circle having the same radius, the angle of the sector is

A. 65o 24′

B. 64o 24′

C. 63o 24′

D. 62o 24′

16. The value of tan -1x + cot -1x is

A. π/3

B. π/6

C. 2π/3

D. 2π

17. If a circle cuts a rectangular hyperbola xy = c2 in A, B, C, D and the parameters of these four points be t1, t2, t3 and t4 respectively, then

A. t1 t2 = t3 t 4

B. t1 t2 t3 t4 = 1

C. t1 = t2

D. t3 = t4

18. If the normal to y2 = 12x at (3, 6) meets the parabola again in (27, -8) and the circle on the normal chord as diameter is

A. x2 + y2 + 30x + 12y -27 = 0

B. x2 + y2 + 30x + 12y + 27 = 0

C. x2 + y2 – 30x – 12y – 27 = 0

D. x2 + y2 – 30x + 12y -27 = 0

19. If the normal any point P on the ellipse cuts the major and the minor axes in G and g

respectively and C be the centre of the ellipse, then

A. a2 (CG)2 + b2 (Cg)2 = (a2 – b2)2

B. a2 (CG)2 – b2 (Cg)2 = (a2 – b2)2

C. a2 (CG)2 – b2 (Cg)2 = (a2 + b2)2

D. none of the above

20. The point of intersection of the tangent at the end of the latus rectum of the parabola y2 = 4x is

A. (-1, 1)

B. (1, 1)

C. (-1, 0)

D. (0, 0)

21. If a, b, c are distinct positive numbers, then the expression (b + c – a)(c + a – b)(a + b – c) -abc is

A. positive

B. negative

C. both negative and positive

D. none of the above

22. If A and B be any two sets, then (A ∪ B)’ is equal to

A. A ∩ B

B. A ∪ B

C. A’ ∩ B’

D. A’ ∪ B’

23. If A = {1, 2, 3, 4}then which of the following are functions from A to itself?

A. f4 = { (x, y) : x + y = 5 }

B. f3 = { (x, y) : y < x }

C. f2 = { (x, y) : x + y > 4 }

D. f1 = { (x, y) : y = x + 1 }

24. The solution of 6 + x – x2 > 0 is

A. -1 < x < 2

B. -2 < x < 3

C. -2 < x < -1

D. none of the above

25. The first term of a G.P., whose second term is 2 and sum to infinity is 8, will be

A. 6

B. 3

C. 4

D. 1

26. Equation of circle having diameters 2x – 3y = 5 and 3x – 4y = 7, and radius 8 is

A. x2 + y2 – 2x + 2y – 62 = 0

B. x2 + y2 + 2x + 2y – 2 = 0

C. x2 + y2 + 2x – 2y +62 = 0

D. none of the above

27. A and B are points in the plane such that PA/PB = K (constant) for all P on a circle. The

value of K cannot be equal to

A. -1/2

B. ½

C. -1

D. 1

28. If the centroid and circumcentre of a triangle are (3, 3) and (6, 2) respectively, then the

orthocentre is

A. (-3, 5)

B. (-3, 1)

C. (3, -1)

D. (9, 5)

29. If sin x + cos x = 1/5, 0 ≤ x ≤ π, then tan x is equal to

A. – 4/3 or -3/4

B. 4/3

C. 4/5

D. none of the above

30. If r1, r2, r3 in a triangle be in H.P., then the sides are in

A. H.P.

B. A.P.

C. G.P.

D. none of the above

31. cot θ = sin 2θ (θ ≠ nπ, n integer) if θ equals

A. 45 degree and 90 degree

B. 45degree and 60 degree

C. 90 degree only

D. 45 degree

32. In an entrance test, there are multiple choice questions. There are four possible answers to each question of which one is correct. The probability that a student knows the answer to a question is 90%. If he gets the correct answer to a question, then the probability that he was guessing is

A. 1/9

B. 36/37

C. 1/37

D. 47/40

33. The value of tan [cos -1 (4/5) + tan -1 (2/3)] is

A. 16/7

B. 6/17

C. 7/16

D. none of the above

34. At x = 5π/6, f(x) = 2 sin 3x + 3 cos 3x is

A. zero

B. maximum

C. minimum

D. none of the above

35. If a < 0, the function (eax + e-ax) is a strictly monotonically decreasing function for values of x is given by

A. x < 1

B. x > 1

C. x < 0

D. x > 0

36. ∫ [sin (log x) + cos (log x)] dx is equal to

A. sin (log x) + cos (log x) + c

B. sin (log x) + c

C. x cos (log x) + c

D. none of the above

37. Solution of differential equation xdy – ydx = 0 represents

A. parabola whose vertex is at origin

B. circle whose centre is at origin

C. a rectangular hyperbola

D. straight line passing through origin

38. If h(x) = f(x) + f(-x), then h(x) has got an extreme value at a point where f ‘(x) is

A. even function

B. odd function

C. zero

D. none of the above

39. If x = 1/3, then the greatest term in the expansion of (1 + 4x)8 is

A. 3rd term

B. 6th term

C. 5th term

D. 4th term

39. Roots of x2 + k = 0, k < 0 are

A. real and equal

B. rational

C. real and distinct

D. equal

40.1 In a quadratic equation with leading coefficient 1, a student reads the coefficient 16

of x strongly as 19 and obtains the roots as -15 and – 4. The correct roots are

A. 8, 8

B. 6, 10

C. – 6, – 10

D. – 8, – 8

41. The value of m for which the equation x2 – mx2 + 3x – 2 = 0 has two roots equal in

magnitude but opposite in sign is

A. 4/5

B. 3/4

C. 2/3

D. 1/2

42. If 1/(b-a) + 1/(b-c) = 1/a + 1/c, then a, b, c are in

A. H.P.

B. G.P.

C. A.P.

D. none of the above

43. If every term in G.P. is positive and also every term in the sum of two proceeding terms,

then the common ratio of the G.P. is

A. (1 – √5)/2

B. (√5 +1 )/2

C. (√5 – 1)/2

D. 1

44. If y = – (x3 + x6/2 + x9/3 + ……), then

A. x3 = 1 – ey

B. x3 = log(1 + y)

C. x3 = ey

D. x3 = 1 + ey

45. Vinay, Manish, Rahul, and Sumit have to give speeches in a class. The teacher can arrange the order of their presentation in

A. 12 ways

B. 24 ways

C. 4 ways

D. 256 ways

46. There are n (>2) points in each of two parallel lines. Every point on one line is joined to every point on the other line by a line segment drawn within the lines. The number of points (between the lines) in which these segments intersect is

A. nC2 x nC2

B. 2nC2 – 2(nC2)

C. 2nC2 – 2(nC1) + 2

D. none of the above

47. The number of ways in which 7 persons can sit around a table so that all shall not have the same neighbours in any two arrangements is

A. 360

B. 720

C. 270

D. 180

48. The length of sub normal to the parabola y2 = 4ax at any point is equal to

A. a√2

B. 2√2a

C. a/√2

D. 2a

49. The expansion of (8 – 3x)3/2 in terms of power of x is valid only if

A. x > 8/3

B. | x | < 8/3

C. x < 3/8

D. x < 8/3

50. If y = – (x3/2 + x3 – x4/4 + ……), then x is

A. ey – 1

B. log1

C. ey + 1

D. ey

51. If a, b, c are in G.P., then logam, logbm, logcn are in

A. G.P.

B. H.P.

C. A.P.

D. none of the above

52. If A is a matrix of order 3 x 4, then each row of A has

A. 12 elements

B. 3 elements

C. 7 elements

D. 4 elements

53. If A, B, C are any three matrices, then A’ + B’ + C’ is equal to

A. A + B + C

B. (A + B + C)’

C. – (A + B + C)

D. a null matrix

54. If A is any matrix, then the product A.A, i.e., A2 is defined only when A is a matrix of order

A. m > n

B. m = n

C. m < n

D. m ≥ n

55**. **The area of the parallelogram of which i and i+ j are adjacent s

A. √2

B. 1/2

C. 2

D. 1

56. If the direction cosines of line are (1/c, 1/c, 1/c), then

A. 0 < c < 1

B. c > 2

C. c > 0

D. ± √ 3

57. Constant term in the expansion of (x – 1/x)10 is

A. 152

B. – 152

C. – 252

D. 252

58. The latus rectum of the ellipse 5×2 + 9y2 = 45 is

A. 5/3

B. 10/30

C. (2√5)/3

D. √5/3

59. i2 + i4 + i6 + …….. (2n + 1) terms =

A. – 1

B. 1

C. – i

D. i

60. If the sum of the series 2, 5, 8, 11, …… is 60100, then n is

A. 100

B. 200

C. 150

D. 250

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